What is Line?
Show Hint
- Distance between three dots
- Distance between two dots
- Straight line
- None of these
The Correct Option is C
Solution and Explanation
Step 1: Understanding the definition of a line
A line is a geometric figure that extends in both directions infinitely and has no endpoints.
It is typically defined as the path traced by a moving point in a single direction.
Step 2: What is the minimum number of points to define a line?
A line can be defined using any two points.
Once we have two points, a straight line can be drawn connecting them.
Step 3: Evaluating the options
(A) Distance between three dots $\Rightarrow$ A curve can pass through three points; not necessarily a line.
(B) Distance between two dots $\Rightarrow$ This defines a line segment, not an infinite line.
(C) Straight line $\Rightarrow$ This is the correct conceptual and geometric definition.
(D) None of these $\Rightarrow$ Incorrect, as (C) is correct.
\[
\boxed{\text{Correct Answer: (C) Straight line}}
\]
Top Questions on Lines
- The line \( x = 1 + 5\mu, y = -5 + \mu, z = -6 - 3\mu \) passes through which of the following points?
- If the straight lines $ \frac{x - 2}{1} = \frac{y - 3}{1} = \frac{z - 4}{-t} \quad \text{and} \quad \frac{x - 1}{t} = \frac{y - 4}{2} = \frac{z - 5}{1} \quad \text{are intersecting, then $ t $ can have:} $
- Find a unit vector in the direction of \( \overrightarrow{DA} \).
- If the lines \[ \frac{x - 1}{-3} = \frac{y - 2}{2k} = \frac{z - 3}{2} \] and \[ \frac{x - 1}{3k} = \frac{y - 1}{1} = \frac{z - 6}{-7} \] are perpendicular to each other, find the value of \( k \) and hence write the vector equation of a line perpendicular to these two lines passing through the point \( (3, -4, 7) \).
- Find the distance between the line \[ \frac{x}{2} = \frac{2}{y - 6} = \frac{1}{-z - 1} \] and another line parallel to it passing through the point \( (4, 0, -5) \).
Questions Asked in UP Board X exam
The sum of a two-digit number and the number obtained by reversing the digits is $88$. If the digits of the number differ by $4$, find the number. How many such numbers are there?
OR
The length of a rectangular field is $9$ m more than twice its width. If the area of the field is $810\ \text{m}^2$, find the length and width of the field.
- UP Board X - 2025
- Pair of Linear Equations in Two Variables
In the figure, $DE \parallel AC$ and $DF \parallel AE$. Prove that $\dfrac{BF}{FE} = \dfrac{BE}{EC}$.
- UP Board X - 2025
- Similarity of Triangles
A solid is a cone standing on a hemisphere with both radii $2$ cm and the slant height of the cone $=2\sqrt{2}$ cm. Find the volume of the solid. (Use $\pi=3.14$)
- UP Board X - 2025
- Surface Areas and Volumes
The shadow of a tower on level ground is $30\ \text{m}$ longer when the sun's altitude is $30^\circ$ than when it is $60^\circ$. Find the height of the tower. (Use $\sqrt{3}=1.732$.)
- UP Board X - 2025
- Heights and Distances
The following table shows the ages of the patients admitted in a hospital during a year. Find the mode and the median of these data.
\[\begin{array}{|c|c|c|c|c|c|c|} \hline Age (in years) & 5-15 & 15-25 & 25-35 & 35-45 & 45-55 & 55-65 \\ \hline \text{Number of patients} & \text{6} & \text{11} & \text{21} & \text{23} & \text{14} & \text{5} \\ \hline \end{array}\]- UP Board X - 2025
- Mean, median, mode and standard deviation